Question

Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a club.

1. Are these events independent?
   1. Input Yes or No:

1. Determine the probability of drawing a diamond and then a club without replacement.
   Write your answer in decimal form, rounded to four decimal places as needed.
   1. Answer =

Linda draws a diamond from a standard deck of 52 cards. She returns the diamond to the deck, then draws a second card. Her second card is a club.

1. Are these events independent?
   1. Input Yes or No:

1. Determine the probability of drawing a diamond and then a club with replacement.
   Write your answer in decimal form, rounded to four decimal places as needed.
   1. Answer =

Box 1: Enter your answer as letters. Examples: A B C, linear, a cat

Box 2: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 3: Enter your answer as letters. Examples: A B C, linear, a cat

Box 4: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172

Answer 1

Answer to 1st question:

The event drawing a Diamond has no relation to the event of drawing a Club Card.

Hence, the two events are Independent.

The answer is YES

There are a total of 13 diamonds and 13 clubs in a pack of 52 cards.

Probability of picking a Diamond card = 13C1 / 52C1 = 13/52 = 1/4

Now, Probability of picking a Club = 13C1 / 51C1 = 13/51 (card is drawn WITHOUT REPACEMENT)

Total probability = (1/4) x (13/51) = 0.0637

Answer to 2nd question :

Similar, to the previous question

The two events are Independent

The answer is Yes

Probability of picking a Diamond card = 13C1 / 52C1 = 13/52 = 1/4

Now, Probability of picking a Club = 13C1 / 52C1 = 13/52 = 1/4(card is drawn WITH REPACEMENT)

Total probability = (1/4) x (1/4) = 0.0625